Preheat your oven to 180°C (350°F) and grease a 9x9-inch baking pan. (Note: Do not use parchment paper to line the pan, because you will keep the cake in this pan to soak and serve it.)
In a separate small bowl, whisk the hot coffee (or hot water) with the cocoa powder until smooth. Pour this hot mixture into your batter and fold it in gently with a spatula just until combined. Try not to overmix.
Pour the batter into your prepared pan and bake at 180°C (350°F) for 30–40 minutes. A toothpick inserted into the center should come out clean.
Let the cake cool in the pan for about 20 minutes so it is warm, but not boiling hot. Use a fork or a wooden skewer to poke holes all over the top of the cake.
Soak the cake
In a medium bowl, whisk together the sweetened condensed milk, whole milk, and evaporated milk. To prevent lumps, mix your cocoa powder with a tablespoon of warm milk first, then whisk it into the rest of the liquid.
Slowly pour the chocolate milk mixture over the warm cake. Put the cake in the fridge for at least 30 to 60 minutes to let the liquid soak in and allow the cake to cool completely before you frost it.
Make the chocolate whipped cream
In a cold mixing bowl, combine the cold heavy cream, sifted cocoa powder, powdered sugar, and vanilla. Beat with an electric hand mixer on medium-high speed until stiff peaks form.
Spread the whipped cream evenly over the cold cake. Garnish with some chocolate shavings or a little cocoa powder, then slice and serve directly from the pan.
Notes
Hot Coffee vs. Hot Water: I use hot coffee to bloom the cocoa powder because it brings out a much deeper chocolate flavor without making the cake taste like coffee. However, you can swap it for plain hot water if you prefer.
Serve Directly from the Pan: Do not try to take this cake out of the pan. Because of the amount of liquid, it will break apart if you try to lift it. It is meant to be soaked, frosted, and served right out of the baking dish.
Soak While Warm: For the best absorption, poke the holes and pour the milk mixture over the cake while it is still warm (about 20 minutes after baking). A cold cake won't drink up the liquid nearly as well.
How to Dissolve the Cocoa: Cocoa powder does not dissolve easily in cold milk. To prevent dry lumps in your milk soak, whisk the cocoa with a tablespoon of warm milk or water first to form a paste, then whisk that paste into the rest of the milk mixture.
Make Ahead & Chill Time: Let the cake sit in the fridge for at least 4 hours before slicing. If you can make it the day before, even better—the cake gets much creamier, and the flavors settle beautifully overnight.
Storage: Keep the cake covered tightly in the refrigerator for up to 4 days. I do not recommend freezing the cake after it has been soaked and frosted, as the texture of the whipped cream and milk soak will break down when thawed.